二维，三维坐标旋转算法(公式）

本文是有关二维，三维坐标旋转算法笔记。

１．二维坐标旋转。二维坐标旋转公式图下：

void Rotate2(double x1, double y1, double alpha, double& x2, double& y2)
{
	x2 = x1 * cos(alpha) - y1 * sin(alpha);
	y2 = x1 * sin(alpha) + y1 * cos(alpha);
}

２．三维坐标旋转

在处理三维坐标旋转时，使用标准的数学公式是沒有问题的。但是把二维坐标旋转调用三次，也能够实现三维坐标的旋转，而且有易读易懂，処理速度快的长处。

void Rotate3(double x1, double y1, double z1, 
             double alphaX,double alphaY,double alphaZ, 
             double& x2, double& y2, double& z2)
{
	//Z Axis Rotation
	double x3 = x1 * cos(alphaZ) - y1 * sin(alphaZ);
	double y3 = x1 * sin(alphaZ) + y1 * cos(alphaZ);
	double z3 = z1;

	//Y Axis Rotation
	double z4 = z3 * cos(alphaY) - x3 * sin(alphaY);
	double x4 = z3 * sin(alphaY) + x3 * cos(alphaY);
	double y4 = y3;

	//X Axis Rotation
	y2 = y4 * cos(alphaX) - z4 * sin(alphaX);
	z2 = y4 * sin(alphaX) + z4 * cos(alphaX);
	x2 = x4;
}